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The paper deals with the distribution of a random variate resulting from a transformation due to some cases of changing the qualitative experiment into a quantitative one. Suppose that upon the qualitative (quantitative) experiment a random variate $Y(X)$ is defined having the alternative (Poisson) distribution with parameter $Q(\Lambda = -In (1-Q))$; in the paper the distribution of $\Lambda$ and the marginal one of $X$ are dealt with, if $Q$ is a beta-distributed random variate. Frequency and characteristic functions and formulae for moments and cumulants are derived and methods are discussed of estimating both parameter values and the actual value of $\Lambda$ from experimental data.
[1] Fisz M.: Wahrscheinlichkeitsrechnung und mathematische Statistik. Z polštiny přel. J. Wloka. Berlin, VEB Deutscher Verlag der Wissenschaften, 1966.
[2] Janko J.: Statistické tabulky. Praha, NČSAV, 1958. MR 0150924
[3] Pearson K.: Tables for the incomplete $\Gamma$-function. London, Cambridge University Press, 1922. Citováno podle 1.
[4] Слуцкий E. E. : Таблицы для вычисления непольной гамма-функции и функции вероятности. Москва,Издат. AHCCP, 1950. Cit. podle 5. Zbl 1157.76305
[5] Šor J. В.: Statistické metody analýzy a kontroly jakosti a spolehlivosti. Z ruštiny přel. L. Kubát. Praha, SNTL, 1965.
[6] Таблицы логарифмической производной гамма-функции и её производных в комплексной области. Москва, Вычислительный центр AHCCP, 1965. Zbl 1099.01519
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